Relentless Scottie Scheffler kept his head as others around him were losing theirs, but while his main rivals fell away, the spectre of Rory McIlroy loomed in the distance.

However, the Northern Irishman’s six-shot deficit may be too far back even for someone who completed the career Grand Slam at the Masters earlier this year, considering the quality of his quarry.

McIlroy’s description of Scheffler as “inevitable” summed up the situation perfectly, as while the American was not as spectacular as he was on Friday in assuming the lead, his progress to a 67 and a four-shot advantage was serene.

Matt Fitzpatrick, who began the day one behind, briefly drew level after an eagle at the second but he was never able to edge himself in front, and every time he slipped up he was punished by his playing partner, either by moving another shot away or saving an unlikely par.

McIlroy, six groups ahead, rode the wave of home support hyped by three birdies in his first four holes, and while his momentum stalled it was reignited by a monster 56-foot eagle putt – his longest of the week – at the 12th which produced the loudest roar of the tournament.

It was important as he had bogeyed the previous hole in a bizarre incident when his shot from the rough dislodged a previously buried ball.

But it was a stroke of good luck at the 15th which brought his final birdie of the day as, coming out hot from the rough, it bounced against the flagstick and dropped four feet from the hole.

McIlroy mania reached its peak at the 17th. With his burnt orange shirt appearing red on television screens, the sight of him marching out of the packed gallery surrounded by thousands of fans was reminiscent of Tiger Woods.

The crowd were so ramped they went wild as he pitched 33 feet past the hole, offering little chance of birdie, but they believed – as they will continue to do on Sunday.

The Masters champion, however, is a little more realistic.

“Scottie Scheffler, he is inevitable. Even when he doesn’t have his best stuff he has become a compete player,” said McIlroy.

“It’s going to be tough to catch him tomorrow if he keeps playing the way he does, but if I can get out tomorrow with a similar start to today and get the crowd going, hopefully he feels that behind me – and you never know.”

Scheffler looks unshakeable, though. Already with a three-shot lead, he birdied the difficult Calamity Corner 16th for the third successive day and the gap was looking as big as the chasm in front of the par three.

China’s ultra-consistent Haotong Li is his closest challenger, with Fitzpatrick dropping back to nine under – where he started the round – having reached 11 under.

Scheffler reeled off six straight pars but still did not lose his overnight lead before a back-to-back eagle and birdie represented a gear shift.

His back nine included eight pars, and the kind of nerveless saves which have made him one of the most successful and consistent golfers of the last three years – closing out victory the last 10 times he has held the outright 54-hole leads.

“A lot of it is staying patient. I know what I need to do tomorrow and it is a matter of going out and doing it,” said Scheffler, whose three majors wins have all come leading after the third round.

“I’m not thinking about winning The Open when I go to sleep tonight.”

Englishman Tyrrell Hatton got himself to nine under but a bogey at the 16th halted his progress, while slightly further down the leaderboard 52-year-old compatriot Lee Westwood had a round of two halves, going out in 40 before an Open record-equalling 29 for the back nine.

“It was a good back nine, wasn’t it? I’d have taken 29 on the back nine stood on the 10th tee,” he said.

Defending champion Xander Schauffele, who started the day two under having been in danger of missing the cut until a birdie run on his Friday back nine, played the three par-fives in five under with two eagles on the back nine after a birdie at the second.

His 66 moved him to seven under but the two-time major winner accepts he is too far back.

“It would have to be a perfect storm situation, it doesn’t look like any of those boys up front are letting up,” he said.